US President Barack Obama declared a victory for US diplomacy yesterday, hailing the implementation of a nuclear deal that "cut off every single path" for Iran to build a nuclear bomb.

In Tehran, meanwhile, President Hassan Rouhani told his people that the agreement was a vindication of his policy towards the West.

However, the limits of that diplomacy was apparent yesterday as the US imposed fresh penalties on Iran just hours after President Obama lifted all nuclear-related sanctions on Tehran.

The US Treasury barred 11 Iranian "entities and individuals" from using the American banking system as a result of alleged involvement in "procurement on behalf of Iran's ballistic missile programme".

While the US is lifting all nuclear-related sanctions, restrictions remain, related to Iran's alleged sponsorship of terrorism, its human rights record and its missile ambitions. Last year, Iran conducted two ballistic missile tests in breach of United Nations resolutions.

Announcing the nuclear deal yesterday, Mr Obama said: "I decided that a strong, confident America could advance our national security by engaging directly with the Iranian government. We've seen the result."

America and its allies are now relieving Iran of all nuclear-related sanctions, including an EU oil embargo. In return, Iran has surrendered 98pc of its low-enriched uranium and removed two-thirds of 19,500 centrifuges that produce the material. A reactor capable of producing plutonium for a bomb has been filled with concrete, and the International Atomic Energy Agency is exercising greater inspection rights.

"Whereas Iran was steadily expanding its nuclear programme, we have now cut off every single path that Iran could have used to build a bomb," said Mr Obama.

Mr Rouhani promised to secure the removal of sanctions when he won the presidency in 2013. He has fulfilled his pledge before a parliamentary election due on February 26.

"Today we are in an atmosphere where we can have political, economic and legal interaction with the world to the benefit of our national interests," said Mr Rouhani. "We believe in our nation's success."

Iran is producing about 2.9 million barrels of oil a day. The International Energy Agency calculates that it could increase this by 700,000 barrels within 90 days, placing further downward pressure on the global oil price.

Both Mr Obama and Mr Rouhani faced fierce opposition from hardliners during negotiations.

When 10 US Navy sailors were detained last week for straying into Iranian waters, Republican congressmen insisted it was evidence of Iran's continued hostility. Mr Obama said their swift release was proof of a new era of diplomacy.

He also hailed the release of four Americans, including Jason Rezaian, a 'Washington Post' journalist who was held for 18 months, in a prisoner swap in the final hours of the deal's implementation.

Before the EU embargo was imposed in July 2012, more than a quarter of Iran's oil exports went to European countries, notably Greece and Italy.

The country had previously been reduced to selling oil to only four big customers: China, India, Japan and South Korea. Iran now has every chance of increasing its exports, the central pillar of its economy.

In Tehran, hardliners had consistently argued that America and its Western allies would never lift sanctions. They claimed that America's goal was to topple the Islamic regime.